We have just introduced Parisian down-and-in options with a call feature, denoted here C D I P

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We have just introduced Parisian down-and-in options with a call feature, denoted here $C_{D I P a}$ . One can also define Parisian up-and-in options $P_{UIPa}$ with a put feature, i.e., with payoff ${(K - S_{T})}^{+} 1_{{G_{D}^{+, L} < T}}$ . Prove the symmetry formula

$C_{D I P a} (S_{0}, K, L; r, δ; D, T) = K S_{0} P_{U I P a} (S_{0}^{- 1}, K^{- 1}, L^{- 1}, δ, r; D, T)$

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